Geological surveys involving generators of seismic waves and detectors of their reflections in the ground are often conducted to determine the position of oil reservoirs and/or to get to know the composition and thickness of the many layers that form the underground. Seismic reflection techniques consist in generating a seismic wave that propagates through the ground and reflects at the interfaces thereof. A precise measurement of these echoes and more specifically of their arrival times enables a determination of the shape, depth and composition of the layers that the seismic waves went through.
In a first phase following the measurement of these data signals, image generation algorithms, well-known in the art, are used to reconstruct a raw picture of the underground in the form of seismic images, sometimes also referred to as echographic images. These images can be either two-dimensional in shape or three-dimensional. Such seismic images comprise pixels the intensity of which is correlated to a seismic wave amplitude, dependent on the local impedance variation.
Geophysicists are used to manipulating such seismic images displaying information relating to amplitude. By merely looking at such seismic images, a geophysicist is capable of identifying areas of the underground having distinct characteristics, and use these to determine the corresponding structure of the underground.
Automatic techniques for extracting structural information from seismic images are known. These generally involve seismic horizon reconstruction algorithms that analyze amplitude gradients in a seismic image and extract the tangent of the local dip in a direction that is transverse to that gradient. Examples of techniques used for reconstructing a seismic horizon using a seismic image are for example described in the French patent FR 2 869 693 and US application US 20130083973.
Sometimes the exact depth of a layer can be known due to other data inputs or because of reliable geological information. Therefore, it is sometimes useful to define fixed related control points on a seismic image which are known to belong to a seismic horizon. It is then useful to compute a seismic horizon by implementing a seismic reconstruction algorithm with imposed conditions on a certain limited number of related control points.
One method for reconstructing a seismic horizon with imposed conditions on a number of related control points is described in the article “Flattening with geological constraints” in Annual Meeting Expanded Abstracts, Society of Exploration Geophysicists (SEG), 2006, pp. 1053-1056 by J. Lomask and A. Guitton.
The method disclosed in this article considers a global approach by solving a two-dimensional nonlinear partial derivative equation relied on local dip. The partial derivative equation is solved using a Gauss-Newton approach by an iterative algorithm whose crucial step is the resolution of a Poisson equation. The approach is global in that it systematically computes a seismic horizon on the entire domain of the seismic image, no matter the number of related control points received as input.
Even if it provides realistic seismic horizons, the method proposed by Lomask et al. suffers from two major drawbacks: its computational cost is often prohibitive for large data volumes, and it requires solving an iterative algorithm on the entire domain of the seismic image every time a change occurs in the number and/or position of the related control points received as input.
The high computational cost of the horizon reconstruction algorithm implemented by Lomask is further increased by the computational means for solving the Poisson equation that forms the core step of the iterative algorithm. In general, another iterative algorithm may be used to solve the Poisson equation. The method disclosed by Lomask therefore comprises an iterative algorithm within another iterative algorithm.
To overcome these drawbacks, an enhancement of the determination of a seismic horizon that optimizes the computational speed of the horizon reconstruction algorithm is sought.